Three new rejection sampling methods for generating samples from the adjoint Klein-Nishina cross section are discussed: the two-branch rejection sampling procedure, the three-branch linear rejection sampling procedure and the three-branch inverse rejection sampling procedure. These methods have all been implemented in the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). The efficiency and sample generation rate of each of these methods are evaluated to characterize the methods and to make recommendations regarding their use. The use of these methods in realistic transport simulations is also evaluated by incorporating a scattering function into the sampling process. The results of an infinite medium problem are presented to verify that the sampling procedure can be used in an adjoint Monte Carlo simulation to generate results that are in agreement with an equivalent forward simulation.